XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-25-180-500-42-ext
Number of variables: 40
Number of constraints: 180
Satisfiable: True
Timestamp: 2025-07-20 22:09:28
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 180

General features

Coarse blocks: 9,000
Value tables: 40

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 360 MAX VALUE 124.77 0.00 0.00 0.00

Coarse blocks size 3 22 12.48 12.00 112,364 MAX VALUE 22,528.10 2.51 0.20 2.34

Relational linkage 0.12 0.56 0.36 0.36 355.76 0.00 -1,049.47 0.06 0.17 1.85

Tightness 0.44 0.56 0.50 0.50 90.11 0.00 -124.72 0.02 0.04 3.83

Tuples 277 351 312.12 314.00 56,182 MAX VALUE 1,033.64 13.61 0.04 3.83

Values 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Value table constraints 4 14 9.00 9.00 360 2.50e+37 86.11 2.58 0.29 2.28

Value table partitions 25 25 25.00 25.00 1,000 MAX VALUE 128.75 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	360	MAX VALUE	124.77	0.00	0.00	0.00
Coarse blocks size	3	22	12.48	12.00	112,364	MAX VALUE	22,528.10	2.51	0.20	2.34
Relational linkage	0.12	0.56	0.36	0.36	355.76	0.00	-1,049.47	0.06	0.17	1.85
Tightness	0.44	0.56	0.50	0.50	90.11	0.00	-124.72	0.02	0.04	3.83
Tuples	277	351	312.12	314.00	56,182	MAX VALUE	1,033.64	13.61	0.04	3.83
Values	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00
Value table constraints	4	14	9.00	9.00	360	2.50e+37	86.11	2.58	0.29	2.28
Value table partitions	25	25	25.00	25.00	1,000	MAX VALUE	128.75	0.00	0.00	0.00

Tree decomposition

Number of clusters: 20
Number of leaves: 9
Tree depth: 4
CIR: 0.10
Independent Cluster Pairs: 17
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 4 58 21.35 15.00 427 2.87e+24 56.32 15.50 0.73 2.93

Variables per cluster 5 21 11.00 9.00 220 1.21e+20 46.24 4.70 0.43 2.46

Separator constraints 0 45 12.35 6.00 247 0 None 12.88 1.04 2.25

Separator variables 0 19 9.00 8.00 180 0 None 4.59 0.51 2.46

Clusters per var 1 13 5.50 6.50 220 8.98e+23 55.15 3.63 0.66 2.24

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	4	58	21.35	15.00	427	2.87e+24	56.32	15.50	0.73	2.93
Variables per cluster	5	21	11.00	9.00	220	1.21e+20	46.24	4.70	0.43	2.46
Separator constraints	0	45	12.35	6.00	247	0	None	12.88	1.04	2.25
Separator variables	0	19	9.00	8.00	180	0	None	4.59	0.51	2.46
Clusters per var	1	13	5.50	6.50	220	8.98e+23	55.15	3.63	0.66	2.24

Dual tree decomposition

Number of clusters: 38
Number of leaves: 14
Tree depth: 6
CIR: 0.20
Independent Cluster Pairs: 135
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 16 378 123.89 107.00 4,708 MAX VALUE 174.08 85.10 0.69 3.56

Variables per cluster 8 88 28.87 22.00 1,097 MAX VALUE 121.11 18.81 0.65 3.09

Separator constraints 0 198 82.50 74.50 3,135 0 None 50.93 0.62 3.46

Separator variables 0 62 24.13 20.50 917 0 None 14.37 0.60 3.13

Clusters per variable 1 11 6.09 7.00 1,097 MAX VALUE 296.23 2.71 0.44 2.22

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	16	378	123.89	107.00	4,708	MAX VALUE	174.08	85.10	0.69	3.56
Variables per cluster	8	88	28.87	22.00	1,097	MAX VALUE	121.11	18.81	0.65	3.09
Separator constraints	0	198	82.50	74.50	3,135	0	None	50.93	0.62	3.46
Separator variables	0	62	24.13	20.50	917	0	None	14.37	0.60	3.13
Clusters per variable	1	11	6.09	7.00	1,097	MAX VALUE	296.23	2.71	0.44	2.22

Primal graph

Density: 23.08%
MCB compute time (ms): 4
MCB cycles: 162
Triangles: 126
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.60 0.24 0.24 9.59 0.00 None 0.09 0.39 3.25

Degree 4 14 9.00 9.00 360 2.50e+37 86.11 2.58 0.29 2.28

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.31 3.00 536 MAX VALUE 192.23 0.49 0.15 0.66

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.60	0.24	0.24	9.59	0.00	None	0.09	0.39	3.25
Degree	4	14	9.00	9.00	360	2.50e+37	86.11	2.58	0.29	2.28
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.31	3.00	536	MAX VALUE	192.23	0.49	0.15	0.66

Triangulated primal graph

Density: 50.00%
MCB compute time (ms): 10
MCB cycles: 352
Triangles: 2,261

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.61 1.00 0.83 0.82 33.24 0.00 -7.77 0.11 0.14 3.06

Degree 4 32 19.50 25.50 780 MAX VALUE 112.02 9.40 0.48 2.83

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 1,056 MAX VALUE 386.71 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.61	1.00	0.83	0.82	33.24	0.00	-7.77	0.11	0.14	3.06
Degree	4	32	19.50	25.50	780	MAX VALUE	112.02	9.40	0.48	2.83
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	1,056	MAX VALUE	386.71	0.00	0.00	0.00

Dual graph

Density: 9.76%
MCB compute time (ms): 269
MCB cycles: 1,679
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.43 0.64 0.51 0.50 91.24 0.00 -122.70 0.03 0.07 4.28

Degree 7 26 17.48 18.00 3,146 MAX VALUE 511.05 3.51 0.20 2.64

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.18 3.00 5,335 MAX VALUE 1,928.56 0.42 0.13 0.49

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.43	0.64	0.51	0.50	91.24	0.00	-122.70	0.03	0.07	4.28
Degree	7	26	17.48	18.00	3,146	MAX VALUE	511.05	3.51	0.20	2.64
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.18	3.00	5,335	MAX VALUE	1,928.56	0.42	0.13	0.49

Minimal dual graph

Density: 1.99%
MCB compute time (ms): 74
MCB cycles: 141

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.33 0.01 0.00 1.20 0.00 None 0.04 6.02 0.18

Degree 2 5 3.56 4.00 640 MAX VALUE 224.30 0.74 0.21 1.11

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.77 7.00 955 MAX VALUE 267.28 1.16 0.17 1.48

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	1.20	0.00	None	0.04	6.02	0.18
Degree	2	5	3.56	4.00	640	MAX VALUE	224.30	0.74	0.21	1.11
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.77	7.00	955	MAX VALUE	267.28	1.16	0.17	1.48

Triangulated dual graph

Density: 46.41%
Triangles: 197,659

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.69 1.00 0.83 0.81 150.14 0.00 -33.58 0.09 0.10 4.72

Degree 7 132 83.07 90.00 14,952 MAX VALUE 759.00 40.90 0.49 3.96

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.69	1.00	0.83	0.81	150.14	0.00	-33.58	0.09	0.10	4.72
Degree	7	132	83.07	90.00	14,952	MAX VALUE	759.00	40.90	0.49	3.96
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.86%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.50 1.00 0.80 0.76 144.13 0.00 -43.36 0.15 0.19 3.30

Degree 2 65 21.22 7.00 3,820 MAX VALUE 421.43 23.43 1.10 3.12

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	1.00	0.80	0.76	144.13	0.00	-43.36	0.15	0.19	3.30
Degree	2	65	21.22	7.00	3,820	MAX VALUE	421.43	23.43	1.10	3.12
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.49%
MCB compute time (ms): 46
MCB cycles: 141
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.5/normalized-rand-2-40-25-180-500-42-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 14 3.27 2.00 720 MAX VALUE 210.88 2.92 0.89 0.89

Eccentricity None None None None None None None None None None

MCB cycle size 6 10 6.45 6.00 910 MAX VALUE 261.78 0.87 0.13 0.56

XCSP 2.1 Benchmarks